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204 110.1 Paired T tests

# 204 110.1 Paired T tests - following results Batt er Bat A...

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11.1 Paired T tests, Comparison of Two Means From Dependent Samples There are instances when we want to use the t test to compare two means; however the test is complicated by confounding variables. For example, two types of baseball bat are compared and the question is asked; which bat will hit a ball further? One experimental design randomly divides the twenty batters into two groups of ten (A and B) and the average distance for each group is calculated. A problem with this design is that most of the differences in distances are due to the batter and not the bat. To eliminate the variation among batters The confounding variable), all 20 batters can use each bat then only the difference in distances between the bats for each batter is tested. For example, assume we have the
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Unformatted text preview: following results. Batt er Bat A Distance Bat B Distance B - A 1 173 189 16 2 174 194 20 3 186 182-4 4 148 164 16 5 175 193 18 6 155 152-3 7 142 154 12 8 130 142 12 9 160 167 7 10 186 202 16 11 165 174 9 12 153 168 15 13 168 173 5 14 142 154 12 15 148 157 9 16 201 220 19 17 166 184 18 18 167 170 3 19 175 186 11 20 178 186 8 mean 164.6 175.55 10.95 std. dev 17.52111508 19.31586476 6.847781047 n 20 20 20 2 sample t t test t = -1.89 t = 7.15 pval = .067 pval = 8.5x10(-7) TI: Use the t test on the list of differences (B-A) PHStat: Use the one sample test for the mean, σ unknown. Note: to use the paired t test the “two” samples must be of equal size and there must be a valid reason for how the data are paired between samples....
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